Rex reminds Anna of her dog.
Rex rappelle son chien à Anna.
The English sentence nearly made my head explode :-), it seems really ambiguous to me. In this example it's slightly clearer because Rex and Anna are different sexes, but if you wrote:
Rex reminds Chris of his dog.
Rex rappelle son chien à Chris.
it becomes really ambiguous. I imagine it would be said by someone (say Bob) talking about about three other parties (Rex, Chris and a dog). It would be clearer if there was more context as to who or what Rex, Chris and the dog were, but as it stands it can be interpreted multiple ways. It's unclear to me if the dog belongs to Rex or Chris, and the meaning changes depending on whether Rex is a dog or a person. The sentence needs a bit more context to try and remove the ambiguity e.g.:
Bob said that his dog Rex reminds Chris of his dog.
Bob said that his friend Rex reminds him of Chris' dog.
It seems the French is less ambiguous in this case, and you need to be careful with translating the French into English.
